This book computes the first- and second-order derivative matrices of
skew ray and optical path length, while also providing an important
mathematical tool for automatic optical design. This book consists of
three parts. Part One reviews the basic theories of skew-ray tracing,
paraxial optics and primary aberrations - essential reading that lays
the foundation for the modeling work presented in the rest of this book.
Part Two derives the Jacobian matrices of a ray and its optical path
length. Although this issue is also addressed in other publications,
they generally fail to consider all of the variables of a non-axially
symmetrical system. The modeling work thus provides a more robust
framework for the analysis and design of non-axially symmetrical systems
such as prisms and head-up displays. Lastly, Part Three proposes a
computational scheme for deriving the Hessian matrices of a ray and its
optical path length, offering an effective means of determining an
appropriate search direction when tuning the system variables in the
system design process.